There is known a traditional cooling system of an internal combustion engine, which includes a generally forwardly inclined cylinder provided in the engine; an oil jacket formed in a cylinder head joined to the cylinder and adapted to cool the cylinder head; an oil cooler disposed forward of the engine; and a thermostat that exercises such control as to introduce or divert oil to or from the oil cooler. In addition, the thermostat is directly attached to the front of the crankcase. Oil having passed through the oil jacket is discharged to the front of the cylinder head, i.e., of the engine. The oil discharged forward of the engine is passed through the thermostat and then delivered to the oil cooler or to a bypass passage bypassing the oil cooler depending on temperature conditions (See e.g. Japanese Patent Laid-open No. 2006-97612).
However, in the cooling system of the internal combustion engine described in Japanese Patent Laid-open No. 2006-97612, although the oil temperature is controlled by the thermostat, a route between the downstream of the thermostat and a cooling portion is long. Thus, it is difficult to supply the oil thus temperature-controlled to the cooling portions. In addition, the oil that has cooled the cylinder head is allowed to pass through the oil cooler and then is returned to the oil pan. Thereafter, oil is again supplied by an oil pump to the cooling portion of the cylinder head; therefore, the oil cooled by the oil cooler is heated by the engine before the oil reaches the cooling portions again. Thus, it is difficult to improve the cooling efficiency of the cooling portion.